Extending a 1D Hamiltonian traveling-wave tube model to laser-driven proton acceleration in helical coil targets: Evaluation of self-consistency effects

This paper investigates the impact of self-consistency in modeling the laser-driven post-acceleration of proton beams using a helical coil target (HC). We adapt and apply the 1D Hamiltonian multi-particle traveling-wave tube model, DIMOHA, to simulate the HC post-acceleration. While DIMOHA does not incorporate the effects of the radial component of the coil and space charge fields, it effectively captures the axial interaction between accelerated protons and the coil's electric field. A key advantage of DIMOHA is that it is a self-consistent code significantly faster than traditional Particle-In-Cell codes, offering an efficient balance between computational time and modeling accuracy. Using DIMOHA, we present a method to assess the significance of self-consistent effects in the post-acceleration process. Through extensive simulations, we explore various beam densities and RF pulse amplitudes to identify the conditions under which self-consistency becomes critical. Our findings show that in setups with high beam densities, self-induced fields modify proton bunch energies within the range of shot-to-shot experimental fluctuations. Furthermore, under typical TNSA conditions, where the bunch energy remains significantly below the cutoff energy, these effects appear negligible for the high-energy population. Thus, simplified models with precomputed fields can be reliably used to satisfactorily evaluate proton spectra.